What should be done with this? If it comes via Redhill it either delays or follows the 1651 departure. If the 1651 runs to time, Redhill passengers who plan to get the 1647 are no more than 10 minutes later to all of the destinations which the 1647 stops at.
You're spot on. The requirement for the service is perhaps most keenly felt by those travelling up from the Horsham/Crawley area, who can be left with an inconvenient change of trains at Gatwick or Three Bridges. It's not of massive added value for many passengers North of Redhill, due to the timing of the 1651 from Redhill towards London Victoria (which clearly probably won't change any time in the near future, but it might be most useful if it could somehow be scheduled later!).
Clearly this is a problem if you have a 1730 appointment in the Victoria area (I usually get the 1614 from Reigate and change when that is the case rather than connecting into the 1647 from Redhill) or a tight connection somewhere along the route but that can only be solved by the 1647 having better timekeeping.
It is an issue, and you are being made to spend a rather long time making that journey, given the Redhill - London Victoria leg could be done in 27 or 28 mins (in theory). So your leeway for cancellations & connections is quite significant.
What causes its delays? The turnaround looks tight for the Portsmouth portion but that is true all day.
It's not usually turnaround at Portsmouth - if that's going to be an issue, the train is often further amended to turn round as far back as Barnham. It seems particularly prone to ever-increasing minor delays due to congestion on the West Coastway, and then when it gets to Horsham, it's rather late joining up, by which time platform staff might well be busy with something else - and then the train also may sometimes need to wait before accessing Three Bridges. The minor delays on the Coastway are literally caused by whatever flavour of the day is tainting punctuality. Sometimes there are level crossing issues, other signalling problems, train faults... you know what I mean; those 3 just seem most common, in no particular order.
Roll on the post-Thameslink timetable for Redhill - only four (?) years to wait.
But no doubt there may still be issues with congestion at the junctions at Redhill Station, and, to be honest, I can't really see much benefit for this situation even when Platform 0 is built.
(In an ideal world, you'd add a pair of "Fast Relief" lines from Earlswood to Redhill (with a new island replacing Platforms 3 & 4 at Redhill for the existing Platform 3/Slow Line & the new Up Fast Relief, and a side platform for the Down Fast Relief), and then as quadruple track from just North of Redhill to the area near the industrial estates just South of Merstham where the Quarry Line is very nearby. The Fast Relief lines would then cross over onto those - possibly via a dive-under through one of the yards. These yards would have their businesses re-sited to the land of the disused Goods Yards at Redhill, which would have been severed by Platform 0 (at least in part). A small number of sidings could be relayed and connected to the North Downs Line or even the Up Slow - for MPVs, Thunderbirds & test trains.
And how would all this help? Well, for example, late-running fast trains could overtake stoppers which could already have been allowed to leave Redhill, but both could stop there. If there was an incident at Gatwick, there would be more space on the Down Quarry & Down Fast Relief to queue trains, without restricting capacity for stopping services towards Redhill & blocking Stoats Nest Junction. The Down Fast Relief could maybe also open up new diversion routes & opportunities for faster freight & passenger services towards Tonbridge.)